Structure of finite-RSB asymptotic Gibbs measures in the diluted spin glass models

Abstract

We suggest a possible approach to proving the Mézard-Parisi formula for the free energy in the diluted spin glass models, such as diluted K-spin or random K-sat model at any positive temperature. In the main contribution of the paper, we show that a certain small modification of the Hamiltonian in any of these models forces all finite-RSB asymptotic Gibbs measures in the sense of the overlaps to satisfy the Mézard-Parisi ansatz for the distribution of spins. Unfortunately, what is still missing is a description of the general full-RSB asymptotic Gibbs measures. If one could show that the general case can be approximated by finite-RSB case in the right sense then one could a posteriori remove the small modification of the Hamiltonian to recover the Mézard-Parisi formula for the original model.

References in corpus (4)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• The Parisi formula for mixed $p$-spin models
• Structure of 1-RSB asymptotic Gibbs measures in the diluted p-spin models
• A hierarchical version of the de Finetti and Aldous-Hoover representations

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• The Ising spin glass on random graphs at zero temperature: not all spins are glassy in the glassy phase
• Mean Field Spin Glass Models under Weak External Field
• Free energy of a diluted spin glass model with quadratic Hamiltonian
• On the replica symmetry phase of the independent set problem
• The full replica symmetry breaking solution in mean-field spin glass models
• Free energy expansion of the spin glass with finite connectivity for $\infty$ RSB